Suppose that X is a Poisson random variable With = 6

(a) Compute the exact probability that X is less than four.

(b) Approximate the probability that X is less than four and compare to the result in part (a).

(c) Approximate the probability that 8 < X < 12.

Step 1 of 4</p>

Given that X is poisson random variable with

The approximation is good when

The X is approximate normal random variable

The mean

And standard deviation

continuity correction will apply that is

And

Step 2 of 4</p>

a) We have to compute the exact probability that X is less than 4

Exact probability can be obtained from the poisson distribution

=

=

= 0.0025(61)

=0.1525

Hence the exact probability that X is less than 4 is 0.1525